QUESTIONING SELF-LOCATION

Suppose you undergo an experiment in which you are put to sleep and then seven duplicates of you are created, with these duplicates having their hair dyed in the seven colours of the rainbow. Meanwhile, your original body is destroyed, so none of the seven duplicates is spatiotemporally continuous with your prior self. When you wake up after this experiment, you will have some uncertainty about the colour of your hair, because all of the duplicates are psychologically identical and thus, until you look in a mirror to see the colour of your hair, you don’t know which duplicate you are. This is self-locating uncertainty, and if you now assign probabilities to the different possible colours of hair, these probabilities are self-locating credences, encoding your beliefs about which duplicate you now are.

Self-locating reasoning is used in many scientific contexts. For example, physicists working on models of the cosmological multiverse often write down probability distributions over the universes, and then use those distributions to give ‘anthropic’ explanations based on the probability of finding yourself in a universe with certain properties. In these scientific applications, it is usually assumed that there is some rationally compelling way to assign self-locating credences, so they can be used to arrive at scientifically legitimate probabilities.

However, I argue in my BJPS article that in many such cases there is not in fact any rationally compelling way to assign self-locating credences. First, let us distinguish two different kinds of self-location. I’ll use the term ‘centred world’ to refer to a pair consisting of a possible world together with a ‘centre’ within that world—that is, a location in space or time where an observer could possibly be found. Then ‘pure self-locating uncertainty’ will refer to cases in which an observer is uncertain about which centred world they are in, out of a set of centred worlds that all belong to the same possible world. For example, this is the kind of uncertainty we see in the duplication case: you don’t know which duplicate you are, but all of the duplicates you could be exist in the same world. Meanwhile, I’ll use the term ‘superficially self-locating uncertainty’ to refer to cases in which we are uncertain about which centred world we are in, out of a set of centred worlds that all belong to different possible worlds. For example, you have this kind of uncertainty when you wake up and wonder what time it is: you don’t know which centred world you are in, out of a set of centred worlds that have you located at different times, but in every possible world there is exactly one time at which you actually wake up, and so all of these centred worlds must belong to different possible worlds.

The philosophical literature on self-location often doesn’t distinguish between pure and superficially self-locating cases, but they are conceptually very different. In cases of superficially self-locating uncertainty, your actual ‘location’ is determined by a specific physical process, such as the set of biological processes that result in you waking up at a certain time. So in these cases we can determine the appropriate self-locating credences by simply looking at the features of the underlying process that determines the location. But in cases of pure self-locating uncertainty, there isn’t any process that determines your location—in the duplication case, you are not literally ‘dropped’ into one of your duplicates. Thus pure self-locating credences can only be understood from a first-person point of view, when you are actually in one of the centred worlds in question, so you can point to yourself and ask, ‘which world am I in?’. That is, pure self-locating credences can’t be derived from a scientific theory applying to a third-person description.

So is there any rationally compelling way to assign pure self-locating credences? First of all, we might think there is some approach that is rationally compelling for practical reasons, that is, it helps us to achieve our practical goals. But before we can determine which credences will help us with our goals, we first have to decide what our goals are. For example, if you are asked to make a bet about the colour of your hair in the duplication case, you might place the bet with the goal of maximizing the total winnings of all of the duplicates. However, you are not obliged to do this, and sometimes you might actually have good reasons to choose a different kind of goal. For example, suppose you learn that the duplicate with red hair is going to die very shortly after the experiment—in that case, you might prefer to place your bet in a way that only benefits the other duplicates, since the red-haired duplicate won’t live long enough to enjoy her winnings. The important point is that pragmatic rationality can’t tell you which goal you should choose here, because rationality doesn’t prescribe our goals for us; it only tells us how to achieve them once we have chosen them.

Moreover, it turns out that in pure self-locating cases, choosing our practical goals immediately determines what credences we ought to assign. For example, if you want to maximize your winnings over all of the duplicates, you should assign equal credences to all of the duplicates; if you want to benefit the duplicates who don’t have red hair, you should assign equal credences over all the duplicates without red hair. Once you’ve decided on your goal, no further scientific facts or experimental evidence can possibly be relevant to your credences. So in fact pure self-locating credences don’t reflect pragmatic rationality; they just record how much you care about your duplicates. Thus there cannot ever be a way to assign pure self-locating credences that is rationally compelling for practical reasons, because from the practical point of view those credences are just encoding what our goals are.

So pragmatic rationality doesn’t tell us how we ought to assign pure self-locating credences—but perhaps there may be a way of assigning pure self-locating credences that is rationally compelling for epistemic reasons instead? That is, perhaps we can show that some particular way of assigning these credences is the best approach if we are trying to believe true things or to avoid believing false things. In particular, philosophical arguments aiming to demonstrate that we ought to assign self-locating credences in some particular way often appeal to principles that are regarded as basic principles of epistemic rationality, such as the ‘principle of indifference’, which tells us that we should assign equal credences over all relevant centred worlds belonging to the same possible world. For example, in the duplication case, the principle of indifference suggests that you should assign equal credences to all of the duplicates, since they all belong to the same possible world.

Now, the principle of indifference does seem intuitively natural. But we should be cautious, because a similar ‘principle of indifference’ is often applied to scenarios involving non-self-locating uncertainty. This principle says that when we have no information to differentiate between a set of possible outcomes, we should assign equal credences to all of them—so, for example, if you have no reason to think a die is weighted, you should assign equal probability to all six faces. The non-self-locating principle of indifference also seems intuitively natural, but it is subject to a serious objection known as Bertrand’s paradox. The problem is that if we are dealing with a continuous space of possible outcomes, there will always be many different ways to divide this space into individual discrete possibilities, and different partitions will result in different credences when we apply the principle of indifference. For example, in the case of the die you could also divide the outcome space up into just two possibilities, ‘one’ and ‘not one’, and then if you apply the principle of indifference to this partition, you will conclude that the outcome ‘one’ has a probability of 1/2 rather than 1/6. So the principle of indifference won’t deliver an unambiguous verdict unless we know in advance how to partition the outcome space, and there isn’t always a clear way to choose a partition. Moreover, since the space of possible final states is continuous in almost any real situation, Bertrand’s paradox affects nearly all cases of non-self-locating uncertainty.

Given that we encounter this problem with the non-self-locating principle of indifference, we should be wary of similar problems in the self-locating case. In effect, the self-locating principle of indifference assumes that we should always divide up the outcome space in such a way that there is one outcome per centred world, or perhaps one outcome per consciousness. But is that way of dividing the space really rationally compelling? This is far from obvious. Indeed, people working on the many-worlds interpretation of quantum mechanics have suggested that applying the principle of indifference to a partition with one outcome per consciousness isn’t the right way to go—they think we should instead assign credences in proportion to a quantum property known as the mod-squared amplitude. So it’s certainly not apparent to everyone that one outcome per consciousness is the only reasonable option.

Now, in the non-self-locating case, we can check empirically which way of dividing up the space leads to the best predictions, and in practice it usually turns out that the best partition is the one that corresponds to the natural symmetries of the process involved in generating the outcome. For example, if a die is being thrown in a way that doesn’t favour any of the faces, then you should choose a partition that treats all of the faces in the same way, and this leads to the standard result where you assign a probability of 1/6 to each face. So in non-self-locating cases, studying the symmetries of the situation provides a principled way of deciding which partition we ought to use. But we can’t do this in pure self-locating cases, because in such cases there is no process that generates the outcome—you aren’t dropped probabilistically into one of your duplicates, so there is no process that decides which one you are. Thus since the kinds of factors that determine the appropriate partition in non-self-locating cases are missing in pure self-locating cases, we might have to conclude in such cases that no particular choice of partition is better than any other choice, which means that there will be no correct way to apply the principle of indifference. This suggests that this kind of epistemic principle can’t give us unambiguous answers about how we ought to assign pure-self-locating credences, and so there may not be any way of assigning pure self-locating credences that is rationally compelling for epistemic reasons either.

If it is true that there is no rationally compelling way of assigning credences in pure self-locating cases, this will have important consequences for a number of scientific and philosophical questions. For example, there is a long-standing philosophical debate over the simulation hypothesis. This involves arguing that the universe is likely to contain many more simulated consciousnesses than non-simulated consciousnesses, and therefore we ought to believe that we are probably a simulation. But this argument only works if we assume that we are rationally compelled to assign equal credence to all of the consciousnesses compatible with our current experiences. Whereas if there’s no rationally compelling way to assign these pure self-locating credences, then we can simply choose to assign higher credences to the non-simulated consciousnesses, leading us to conclude that we are probably not a simulation. So the simulation argument won’t work unless there is a rationally compelling way to assign the pure self-locating credences in this case. And similar results may apply in other applications of self-locating credences in science, such as the cosmological multiverse or the many-worlds interpretation of quantum mechanics. So it is an important project to determine whether the self-locating credences involved in these applications are pure or superficial, and to decide whether the relevant arguments still work if there is no rationally compelling way to assign the credences.